The radius of gyration of a uniform rod of length \(l,\) about an axis passing through a point \(\frac{l}{4}\) away from the centre of the rod, and perpendicular to it, is

Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is

\(LED\) is constructed from \(Ga-As-P\) semiconducting material. The energy gap of this \(LED\) is \(1.9\, eV\). Calculate the wavelength of light emitted and its colour. \(\left[ h =6.63 \times 10^{-34} \;Js \right.\) and \(\left. c =3 \times 10^{8}\; ms ^{-1}\right]\)

A closely wounded circular coil of radius \(5\,cm\) produces a magnetic field of \(37.68 \times 10^{-4}\,T\) at its center. The current through the coil is \(......A\). [Given, number of turns in the coil is \(100\) and \(\pi=3.14]\)

In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

Identify the logic gate given in the circuit.

For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below

A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm .

A galvanometer of resistance \(100 \Omega\) when connected in series with \(400 \Omega\) measures a voltage of upto \(10 \mathrm{~V}\). The value of resistance required to convert the galvanometer into ammeter to read upto \(10 \mathrm{~A}\) is \(\mathrm{x} \times 10^{-2} \Omega\). The value of \(\mathrm{x}\) is _______.